Question

calculate the expected value of spinning the spinner one time. round to the nearest hundredth if necessary.
sample problem
8(\frac{1}{3}) + 6(\frac{1}{3}) + 4(\frac{1}{3}) = \frac{8}{3}+2 + \frac{4}{3}=6
the expected value is 6.

Explanation:

Step1: Determine probabilities

The spinner is divided into 8 equal - sized sections, so the probability of landing on each section is $\frac{1}{8}$.

Step2: Calculate expected value

The values on the spinner are 1, 2, 3, 4, 4, 5, 5, 6.
The expected value $E(X)$ is calculated as follows:
\[

$$\begin{align*} E(X)&=1\times\frac{1}{8}+2\times\frac{1}{8}+3\times\frac{1}{8}+4\times\frac{2}{8}+5\times\frac{2}{8}+6\times\frac{1}{8}\\ &=\frac{1 + 2+3 + 8+10 + 6}{8}\\ &=\frac{30}{8}\\ & = 3.75 \end{align*}$$

\]

Answer:

3.75